10. Упростите числовое выражение √40√2-57|-√40√2+57|.

$$\left|\sqrt{40\sqrt{2}-57}\right|-\left|\sqrt{40\sqrt{2}+57}\right|$$

Так как $$40\sqrt{2} = \sqrt{1600 \cdot 2} = \sqrt{3200}$$

$$57 = \sqrt{57^2} = \sqrt{3249}$$.

Тогда $$40\sqrt{2} - 57 < 0$$, a $$40\sqrt{2} + 57 > 0$$

$$\left|\sqrt{40\sqrt{2}-57}\right|-\left|\sqrt{40\sqrt{2}+57}\right| = -\sqrt{40\sqrt{2}-57} - \sqrt{40\sqrt{2}+57}$$

Ответ: $$-\sqrt{40\sqrt{2}-57} - \sqrt{40\sqrt{2}+57}$$